Scale is a concept that is found at numerous grade levels in the Nova Scotia Mathematics curriculum. Scale drawings and models, similar polygons, and proportions are all found in mathematics outcomes. In math, scale is the ratio of the length in an image (or model) to the length of the actual object.

Below is a question relating to scale factors. A scale factor is the ratio of any two corresponding lengths in two similar geometric figures. Take a look at the three different versions of Connect Four. Estimate the scale factor between each pair of game boards from the given pictures. Estimate the radius of each of the coloured chips. Is the scale factor of the radius of each coloured chip the same as the scale factor of their volume? ​

Travel Size

Standard Size

Giant Size

You might ask students how scale is different from proportion. Try out this question: How big would a game board of Connect Four Hundred be (or even Connect Four Million) compared to Connect Four?

In visual arts, scale refers to the size ratio between objects within an image. Using a consistent scale will make a drawing look more realistic. Objects do not appear too large or too small when compared to each other. Sometimes however, an artist might intentionally change the scale of certain objects in an image. One such technique is called 'Hieratic scale' or sometimes 'Hierarchical proportion'. This technique can be seen in paintings and sculpture from the middle ages where powerful or holy people were sometimes painted larger than ordinary or less important people to show their relative importance. The larger a person was, the greater their importance.

The painting to the left is titled 'Saint Lawrence Enthroned with Saints and Donors.' It was painted by the Italian artist Fra Filippo Lippi in the fifteenth century. The central figure of this painting is Saint Lawrence who is significantly larger than all the other figures in the painting. He is flanked by Saints Cosmas and Damian who are slightly smaller. Smaller still, kneeling in the foreground, are members of the Alessandri family who commissioned this artwork. Using this hieratic scale, the artist quickly establishes Saint Lawrence as the focal point and also indicates the relative importance of the other figures.

Visual artists might also play with scale as it relates to perspective. One way to do this is called a Ponzo Illusion. The brain tends to judge an object's size by its background. Congruent object in different places on an image may appear to be different sizes. This is because of the cues the brain takes from linear perspective.

Which tree appears larger?

It would be fun to show students examples of how visual artists play with scale in order to make an impact on the viewer. Students might even be given an opportunity to create a piece of art that has an exaggerated or inconsistent scale or plays with forced perspective.

Nova Scotia Mathematics Curriculum OutcomesGrade 6 N05 - Students will be expected to demonstrate an understanding of ratio, concretely, pictorially, and symbolically. Grade 8 N04 - Students will be expected to demonstrate an understanding of ratio and rate.Grade 8 N05 - Students will be expected to solve problems that involve rates, ratios, and proportional reasoning.Grade 9 G03 - Students will be expected to draw and interpret scale diagrams of 2-D shapes. Math at Work 10 G03 - Students will be expected to demonstrate an understanding of similarity of convex polygons, including regular and irregular polygons.Mathematics Essentials 11 D9 - calculate scale factors in 2-D scale diagrams and 3-D scale models understand the relationship among the scale factor and the related change in area or volume.Math at Work 11 G02 - Students will be expected to solve problems that involve scale.Mathematics 11 M03 - Demonstrate an understanding of the relationships among scale factors, areas, surface areas and volumes of similar 2-D shapes and 3-D objects.